2012/06/30 by Roberto Auzzi, Shmuel Elitzur, Sven Bjarke Gudnason +1
Physics and Astronomy · #Astrophysical Phenomena and Observations #Back-reaction #Big Crunch #Black Holes and Theoretical Physics #Bounded function #Compactification (mathematics) #Conformal map #Cosmology and Gravitation Theories #Equations of motion #Gravitational singularity #Spacetime #String theory #Torus #hep-th
paper · pdf · doi:10.1007/jhep08(2012)035
published as JHEP 1208:035,2012 · LaTeX, 38 pages, 13 figures. V2: appendix C added, references added and typos corrected
openalex publication_date 2012/08/01 · arxiv created 2012/08/07 · arxiv updated 2012/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons.